Advances in Risk Management

342 LARGE AND SMALL CAP STOCKS IN EUROPE

Table 17.5 Unconditional moment estimates of all markets

Unconditional moment estimates

France Germany Great Britain

Large cap index variance 9.31 11.73 5.52
Small cap index variance 5.30 3.19 3.04

Covariance 4.38 3.41 0.80

Beta coefficient 0.47 0.29 0.15

Correlation 0.62 0.55 0.20

Notes: The beta coefficient is defined as the quotient between the large cap and small cap indices
covariance and the large cap index variance. Variances and covariance are reported in percentage
terms.

17.5 Asymmetries analysis

The asymmetries analysis is carried out in two steps. First, a graphical anal-
ysis of news impact surfaces is displayed. Second, the robust conditional
moment test of Wooldridge (1990) is conducted before and after estimating
the covariance model.
Table 17.5 displays the unconditional moment estimates of all markets in
order to facilitate comprehension of the following sections.

17.5.1 News impact surfaces

The news impact surfaces are the multivariate generalization of the news
impact curves introduced by Engle and Ng (1993) and Hentschel (1995). The
univariate applications plot the conditional variance against the last period’s
shocks. The multivariate generalization plots the conditional variance and
covariance against large- and small-firm shocks from the last period, holding
past conditional variances and covariances constant at their unconditional
sample levels.
Figure 17.3 shows the news impact surfaces for the conditional second
moments and conditional betas obtained from the asymmetric bivariate
GARCH specification. Following Engle and Ng (1993) and Kroner and Ng
(1998), each surface is represented in the regionεi,t=[−5, 5] fori=1, 2. The
news impact surfaces try to reflect the sensitivity of variances, covariances
and betas to the sign and size of the innovations.
Panel (A) of Figure 17.3 displays the news impact surfaces for the French
market. It can be seen that the CAC40 variance increases the most when
cross-signed shocks take place. The MIDCAC variance surface shows a clear
sensitivity to its own negative shocks when positive or negative shocks on